Tire chains are widely used in snow and icy conditions in order to improve a vehicle's traction. One significant problem with tire chains, though, is that many are injurious to wheels and to tire sidewalls. An added problem is the installation and removal of tire chains, a task of sufficient difficulty that professional installation and removal is often required. While removal may be eased with a vehicle's arrival in improved road conditions, installation most often takes place in snow and ice, a factor that can greatly increase installation difficulty. Yet another problem with many tire chains is that the devices are sold in specific sizes in order to fit a given tire and wheel combination, thereby negating fit to anything other than a specific tire and wheel per chain set. The present modular apparatus solves these problems.